lim -7 + (7/x)/ 6 - (1/x2)

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To evaluate the given limit:

lim (-7 + 7/x)/ (6 - 1/x^2)
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We need to find the value that x approaches as it gets very close to -∞ (negative infinity).

First, let's simplify the expression by multiplying the numerator and the denominator by x^2 to eliminate the fractions:

lim (-7x^2 + 7x)/(6x^2 - 1)
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Next, we can factor out x in both the numerator and the denominator:

lim x(-7x + 7)/(x^2(6 - 1/x^2))
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Now, we can cancel out the common factor of x in the fraction:

lim (-7x + 7)/(x(6 - 1/x^2))
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As x approaches -∞, the -7x term becomes dominant, so the limit becomes:

lim (-7x)/(x(6 - 1/x^2))
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Simplifying further, we cancel out the common factor of x:

lim -7/(6 - 1/x^2)
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Now, we can evaluate the limit directly by substituting x with -∞:

lim -7/(6 - 1/(-∞)^2)

Since 1/(-∞)^2 is equal to 0, the expression simplifies to:

lim -7/(6 - 0)
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lim -7/6
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Therefore, the limit of (-7 + 7/x)/ (6 - 1/x^2) as x approaches -∞ is -7/6.